Question

For a purely inductive or a purely capacitive circuit, the power factor is

• A. zero
• B. 0.5
• C. 1
• D. $\infty$

Hint:

Physics Tip: A circuit with a zero power factor is said to have "wattless current" because the average power consumed over a complete cycle is zero.

Answer 1

The Correct Option is A

Concept: Physics (Alternating Current) - Power Factor in Reactive Circuits.

Step 1: Define power factor. The power factor in an AC circuit is defined as the cosine of the phase angle ($\phi$) between the applied voltage and the resulting current: $$\text{Power Factor} = \cos \phi \text{}$$

Step 2: Determine the phase angle for purely reactive circuits.
• Purely Inductive Circuit: The current lags the voltage by exactly $90^{\circ}$ ($\phi = 90^{\circ}$).
• Purely Capacitive Circuit: The current leads the voltage by exactly $90^{\circ}$ ($\phi = -90^{\circ}$).

Step 3: Calculate the power factor. In both cases, the magnitude of the phase angle is $90^{\circ}$: $$\cos(90^{\circ}) = 0 \text{ and } \cos(-90^{\circ}) = 0 \text{}$$

Step 4: Conclusion. Because the phase difference is $90^{\circ}$, the power factor is zero. This means no real power is dissipated; energy simply oscillates between the source and the inductor or capacitor. $$ \therefore \text{The power factor for a purely inductive or capacitive circuit is zero.} \text{} $$